Rf circuit, circuit evaluation method, algorithm and recording medium

ABSTRACT

It is required to qualitatively design a circuitry device in which not only in a small-signal simulation but also in a large-signal simulation, loop oscillation and motorboating oscillation of an amplifier are precisely predicted to suppress oscillation without severing a loop or without inserting a circulator. To remove insertion loss due to a probe resistor Rx, a negative resistor −Rx/2 is arranged at both ends thereof. To prevent consumption of a DC bias in the probe, a DC block is applied. Further, to remove thermal noise caused by an actual resistor to reduce influence on a noise factor NF, the noise temperature (environmental temperature) of the actual resistor is set to zero Kelvin.

TECHNICAL FIELD

The present invention relates to a technique for evaluating electriccircuits such as an amplifier circuit and an oscillator circuit.

RELATED ART

To detect parasitic oscillation of an oscillator and an amplifier on amicrowave circuit simulator, it is required at an arbitrary point of acircuit to attain reflection coefficients (characteristic impedances) inconsideration of a left-side section of the circuit and a right-sidesection thereof. However, if the circuit is separated at the point, thecharacteristic of the circuit differs from the inherent characteristicthereof. Accordingly, a method has been devised in which a tool isinserted in an arbitrary position of a circuit without giving muchinfluence upon the characteristic of the circuit to obtain reflectioncoefficients (impedances) at the point in consideration of a left-sidesection of the circuit and a right-side section thereof. Representativetools are the S-probe by Wang et al and the S-parameter Oscillator TestComponent (equivalent to the S-probe in its actual circuitconfiguration) mounted as a standard item on the microwave circuit CADsoftware ADS of Agilent Technology ([1] K. Wang et al., “The S-Probe ANew, Cost-Effective, 4-Gamma Method for Evaluating Multi-Stage AmplifierStability”, 1992 MTT-S Digest, pp. 829-832).

The S-probe is, as FIG. 1 shows, a 6-port circuit including largeresistors (Rs,Rv) and voltage-dependent power sources M₃ and M₄ and isinserted, by use of ports 1 and 2, in an arbitrary cross section of acircuit to be observed. Assume here that the ports 1 and 2 are connectedrespectively to Z₁ and Z₂ impedances. These impedances can be renderedfrom the passing characteristics from ports 5 and 6 to ports 3 and 4.

Since the resistors Rs and Rv have quite a high resistance value, littlecurrent flows through the ports 6, 5, 4, and 3, which hardly affects thecircuit Z₁ and Z₂. Also, Rx connecting Z₁ and Z₂ in series to each otherhas quite a small value to lower insertion loss as much as possible.

Assuming that current I₂ flows through the circuit Z₂ when voltage V₆ isapplied to the port 6, voltages Va and Vb at nodes A and B at both endsof resistor Rx are

Va=Vb+I ₂ ·Rx=Vb(Z ₂ +Rx)/Z ₂

Vb=I ₂ ·Z ₂.

Additionally, voltage V₃ at the port 3 and voltage V₄ at the port 4 are

V ₃ =−M ₃ ·Vr=−M ₃(Va−Vb)=−VaM ₃ Rx/(Z ₂ +Rx)

V ₄ =−M ₄ ·Vb.

Therefore, the passing characteristics from the port 6 to the ports 3and 4 are

S ₃₆ =V ₃ /V ₆ =−VaM ₃ Rx/[V ₆(Z ₂ +Rx)]

S ₄₆ =V ₄ /V ₆ =−M ₄ Z ₂ Va/[V ₆(Z ₂ +Rx)].

Similarly, assuming that current I₁ flows through the circuit Z₁ whenvoltage V₅ is applied to the port 5, voltages Va and Vb at the nodes Aand B at both ends of resistor Rx are

Va=I₁Z₁

Vb=Va+I ₁ Rx=Va(Z ₁ +Rx)/Z ₁.

In addition, the voltage V₃ at the port 3 and the voltage V₄ at the port4 are

V ₃ =−M ₃ Vr=−M ₃(Vb−Va)=VaM ₃ Rx/(Z ₁ +Rx)

V ₄ =−M ₄ Vb.

Hence, the passing characteristics from the port 5 to the ports 3 and 4are

S ₃₅ =V ₃ /V ₅ =−VbM ₃ Rx/[V ₅(Z ₁ +Rx)]

S ₄₅ =V ₄ /V ₅ =M ₄ Vb/V ₅.

In consequence,

S ₄₆ /S ₃₆ =M ₄ Z ₂ /M ₃ Rx

S ₄₅ /S ₃₅ =−M ₄(Z ₁ +Rx)/(M ₃ Rx).

In the expression,

M ₄/(M ₃ Rx)=1

0<R<<1.

Particularly, by selecting as specific circuit parameters

Rs=10 MΩ

Rv=10 MΩ

Rx=100 μΩ

M₃=1000

M₄=1,

there are obtained

Z ₁ =−S ₄₅ /S ₃₅

Z ₂ =S ₄₆ /S ₃₆.

Therefore, the Z₁ and Z₂ impedances are rendered from the passingcharacteristics from the ports 5 and 6 to the ports 3 and 4. Hence, byviewing the circuit side, forward and backward reflection coefficientsΓ_(S) and Γ_(L) are obtained respectively as

Γ_(S)=(Z ₁ −Z ₀)/(Z ₁ +Z ₀)

Γ_(L)=(Z ₂ −Z ₀)/(Z ₂ +Z ₀).

Here, Z₀ is system impedance and inner resistance of the S parameterprobe and is ordinarily 50 Ω.

Incidentally, there has been proposed a technique in which a capsulateddocument is capsulated as a single document which includes contentinformation, an operation program to make a computer implement variousfunctions, and transmission destination information to send variousinformation pieces to the computer; and by restricting operationprocessing to the content information in the capsulated document, it ispossible to prevent unlawful use of the content information in thecapsulated document and to protect the copyright of the contentinformation (reference is to be made to, for example, Patent Document1). Patent Document 1: Japanese Patent Laid-Open Publication No.2001-177580

DISCLOSURE OF THE INVENTION Problem to be Solved by the Invention

It cannot be considered that the relevant probe circuit which isinserted in an arbitrary section of a circuit on a microwave circuitsimulator to obtain reflection coefficients in the section does notaffect the circuit to be observed at all; however, the more the proberesistance Rx which affects the circuit to be observed is, the more lossin the circuit appears. Hence, it is required that Rx is sufficientlysmall, e.g., 100 μΩ.

If the value of the probe resistance Rx is sufficiently small, e.g., 100μΩ as the typical value described above, the actual insertion loss canbe substantially ignored. Particularly, when a small signal is employedon the circuit simulator, the reflection coefficients (i.e.,characteristic impedances) are determined by the circuit topology in theactual calculation, and the process to calculate the potentialdifference between both ends of the probe resistor is not adopted;hence, even if the probe resistance is quite small, there does not occurany problem in the numerical precision of the potential differencebetween both ends in the numeric calculation. Therefore, in a casewherein the reflection coefficients of a small signal of the circuit areobtained by the relevant S-probe, the S-probe can almost correctlycalculate the reflection coefficients.

However, in a case wherein the reflection coefficients of the circuitare obtained by the S-probe through a large-signal simulation, thereflection coefficients are calculated in an actual calculation based onan input signal to the circuit and a response thereto. Here, since theresistor Rx is employed as a voltage probe, if it is desired to lowerthe resistance value Rx to reduce the influence on the circuit, theretakes place canceling of positions in the potential difference appearingon both ends of the resistor; there hence exists a problem that theresistance value Rx cannot be extremely reduced.

Furthermore, the resistance Rx employed as a voltage probe is set, tolower the insertion loss, to a value remarkably smaller than theordinary resistance component; hence, to obtain a probe voltage forhigh-precision observation, it is inevitable to input a relatively largeprobe signal; this causes perturbation in the circuit to be observed andleads to a situation wherein the reflection coefficients cannot becorrectly obtained in the circuit.

However, it needs not to say that there occurs a dilemma in which theinsertion loss becomes larger if Rx is increased.

Moreover, there also exists a drawback in which the DC bias is notappropriately applied to the circuit to be observed, in the form thatthe bias passes through the probe.

The present invention has been devised to remove the problems describedabove. An exemplary object thereof is to provide an RF circuit, acircuit evaluation method, an algorithm, and a recording medium in whichnot only in a small-signal simulation but also in a large-signalsimulation, loop oscillation and motorboating oscillation of anamplifier can be precisely predicted to quantitatively design acircuitry device to suppress oscillation without severing a loop orwithout inserting a circulator.

Means for Solving the Problem

To achieve the exemplary object, the present invention has features asfollows.

A reflection coefficient measuring circuit (to be referred to as“no-loss S-probe” hereinbelow) proposed here is obtained by improvingthe S-probe by Wang et al; and by canceling the positive resistancecomponent Rx by use of negative resistance, the probe is strictly ano-loss probe in circuit operation. Since the probe is a no-loss probe,it is not required to apply an extremely small value to the value of theprobe resistance Rx. Therefore, to obtain reflection coefficients of acircuit in a large-signal state, the problem of the canceling of thepotential difference at both ends of the probe resistor is removed; itis hence possible to obtain a probe voltage at high precision. That is,the reflection coefficient calculation method employing the no-lossS-probe is capable of attaining reflection coefficients using an inputof a sufficiently small probe signal which hardly causes perturbation inthe circuit; it is also possible in a large-signal state and at anarbitrary point of the circuit to obtain coefficients (characteristicimpedances) in consideration of a left-side section of the circuit and aright-side section thereof quite appropriately when compared with therelevant method.

A first exemplary aspect of the present invention is an RF circuit on anactual circuit or a circuit simulator, including a function for beinginserted by a first port and a second port thereof in a circuit to beobserved, at an arbitrary cross-sectional point of the circuit, andevaluating a reflection coefficient or a characteristic impedance in thecross section, insertion loss between the first port and the second portstrictly being completely zero.

A second exemplary aspect of the present invention is a circuit on anactual circuit or a circuit simulator to be used in a microwave ormillimeter wave range or a high-frequency range, including six RF ports,wherein a first resistor is connected from port 1 to a node a on thecircuit, a second resistor is connected from the node a to a node b, athird resistor is connected from the node b to port 2, a fourth resistoris connected from the node a to a node c, a fifth resistor is connectedfrom the node b to a node d, and a sixth resistor is connected from thenode b to a node e; a first DC block (or a capacitor which has quite alarge capacity value and which passes therethrough an RF signal almostwithout loss) is connected from the node c to port 6, a second DC block(or a capacitor which has quite a large capacity value and which passestherethrough an RF signal almost without loss) is connected from thenode d to port 5, and a third DC block (or a capacitor which has quite alarge capacity value and which passes therethrough an RF signal almostwithout loss) is connected from the node e to a ground point (earth); afirst voltage-dependent power source is connected from port 3 to aground point (earth) and a second voltage-dependent power source isconnected from port 4 to a ground point (earth); assuming that aninstantaneous potential at the node a measured using as a reference thenode b of the second resistor is Vr, there is induced, at the same timeof occurrence of Vr, an instantaneous voltage of a magnitude of M·Vr (Mis a real coefficient) in a direction from a ground point (earth) to theport 3; and assuming that an instantaneous potential at the node bmeasured using as a reference the node e of the sixth resistor is Vb,there is induced, at the same time of occurrence of Vb, an instantaneousvoltage of a magnitude of Vb in a direction from a ground point (earth)to the port 4; and assuming that Rx is a positive real number, Rs is apositive real number and Rs>>1, and α is a real coefficient, the firstand third resistors have resistance values which widely include alsonegative resistance and which are respectively −αRx and (α−1)Rx, and thesecond resistor has a resistance value of Rx, and the four, five, andsixth resistors have a resistance value Rs which is quite larger than asystem resistance.

Additionally, in consideration of the design and evaluation of alow-noise amplifier, the circuit in accordance with the second exemplaryaspect may be a circuit wherein the first to sixth resistors are used atan environmental temperature of absolute zero degree (zero degreeKelvin) or the environmental temperature is set to absolute zero degree(zero degree Kelvin).

Moreover, in relation to the evaluation method regarding stability of acircuit to be observed, by use of the circuit described above, a thirdexemplary aspect of the present invention is an evaluation method or analgorithm on a circuit simulator, wherein by inserting an RF circuit inaccordance with the above exemplary aspects by the first port and thesecond port in a circuit to be observed, at an arbitrary cross-sectionalpoint of the circuit and evaluating a forward or backward reflectioncoefficient (characteristic impedance); and by assuming that the forwardreflection coefficient is Γ_(S) and the backward reflection coefficientis Γ_(L), an absolute value of a product therebetween abs(Γ_(S)·Γ_(L))is or the absolute value of the product and a phase angle of the productphase (Γ_(S)·Γ_(L)) are employed as an index of stability of the circuitto be observed.

In addition, a fourth exemplary aspect of the present invention alsoincludes a measuring method and a measuring apparatus for electriccircuits such as an amplifier circuit and an oscillator circuit, adesigning method and a designing apparatus for the electric circuits, arecording medium having stored therein the measuring method of theelectric circuits, and a recording medium having stored therein thedesigning method of the electric circuits, including the above exemplaryaspects.

As FIG. 2 shows, the probe circuit of the present invention is a 6-portcircuit including a voltage-dependent power source and resistors havinga large resistance value, and the circuit is inserted by use of ports 1and 2 as circuit insertion terminals in an arbitrary point of a circuitthe reflection coefficients of which are to be obtained; referring toFIG. 2, description will be given of perturbation caused in the circuitdue to insertion of this probe in the circuit.

The section between the ports 1 and 2 seems to be completelyshort-circuited (the resistance value is zero) because the resistance Rxis cancelled by −Rx obtained as the sum of the resistor values on bothsides thereof, −αRx and (α−1)RX. On the other hand, since the resistorRs has quite a large value, a current hardly flows through the ports 3,4, 5, and 6 and hence the circuit impedances Z₁ and Z₂ are not affected.By use of a DC block, a correct DC bias may also be applied. Further,the resistor Rx to be inserted in series between the circuits Z₁ and Z₂has a relatively small value, which is cancelled by the negativeresistor −Rx additionally disposed; hence, the insertion loss of thisprobe can be strictly ignored. Moreover, the resistor Rx operates as avoltage probe, but an extremely small value needs not to be employed forRx; it is hence possible to prevent the canceling of the potentialdifference thereat in the numeric calculation. Also, by setting thenoise temperature of each actual resistor to absolute zero degree (zerodegree Kelvin), the influence exerted by this probe onto the noisefactor NF of the circuit is completely zero (required in the design ofLNA). Typical circuit parameters will be favorably selected as

Rs=10 MΩ

Rx=1 Ω

M=1

α=½.

Incidentally, assume that the circuits having impedances Z₁ and Z₂ areconnected respectively to the ports 1 and 2. These impedances arederived from the passing characteristics from the ports 5 and 6 to theports 3 and 4 as

Z ₁ =−S[4,5]S[3,5]−Rx/2

Z ₂ =S[4,6]/S[3,6]+Rx/2.

Therefore, viewing the circuit side, the forward and backward reflectioncoefficients Γ_(S), Γ_(L) are respectively attained as

Γ_(S)=(Z ₁ −Z ₀)/(Z ₁ +Z ₀)

Γ_(L)=(Z ₂ −Z ₀)/(Z ₂ +Z ₀).

Here, Z₀ is system impedance and internal resistance of the S parameterprobe which is ordinarily 50 Ω.

ADVANTAGES OF THE INVENTION

By use of the S-probe of the present invention, not only in asmall-signal simulation but also in a large-signal simulation, looposcillation and motorboating oscillation of an amplifier can beprecisely predicted to quantitatively design a circuitry device tosuppress oscillation without severing a loop or without inserting acirculator. Therefore, the no-loss S-probe of the present invention isquite useful for the designing of a microwave circuit.

BEST MODE FOR CARRYING OUT THE INVENTION EXEMPLARY EMBODIMENT 1

The no-loss S-probe is an ideal probe to be used on a simulator andincludes a voltage-dependent power source, capacitors, and resistors,and the probe is capable of obtaining reflection coefficients (forwardand backward) at an insertion point with strictly zero insertion loss.The no-loss S-probe has in general a 6-port circuit configuration asshown in FIG. 2 and can be inserted, by use of the ports 1 and 2 ascircuit insertion terminals, at an arbitrary point of a circuit thereflection coefficients of which are desired to be obtained.

First, the loss caused in the circuit due to insertion of the probe inthe circuit will be discussed. The section from the port 1 to the port 2seems to be short-circuited because the resistance Rx is cancelled bythe negative resistance −Rx. On the other hand, since the resistor Rshas quite a large value, a current hardly flows through the ports 3, 4,5, and 6 and hence the circuit impedances Z₁ and Z₂ are not affected.

By using a DC block, a correct DC bias may also be applied. Further, theresistor Rx to be inserted in series between the circuits Z₁ and Z₂ hasa relatively small value, which is cancelled by the sum of resistorcomponents added to both sides thereof, i.e. −Rx (the negativeresistor); hence, the insertion loss of this S-probe can be strictlyignored.

In addition, the resistor Rx operates as a voltage probe, but anextremely small value needs not to be employed for Rx due to support ofthe above negative resistance in this method; hence, it is only requiredto apply, as the probing signal, a signal of relatively small powerwhich hardly causes perturbation in the circuit in the large-signalanalysis, leading to a merit that the reflection coefficients(impedances) are obtainable with almost no perturbation (i.e.,correctly) in the large-signal state. Further, by setting the noisetemperature of each actual resistor to absolute zero degree (zeroKelvin), the influence exerted by this S-probe onto the noise factor NFof the circuit is completely zero; and when it is applied to a Low-NoiseAmplifier (LNA), the NF design can be correctly carried out.

In this regard, assume that the circuits having impedances Z₁ and Z₂ areconnected respectively to the ports 1 and 2. These impedances can bederived from the RF passing characteristics from the ports 5 and 6 tothe ports 3 and 4. This will now be proved in a case of a small-signalanalysis employing S-parameter ports.

Assuming that current I₂ flows through the circuit Z₂ when voltage V₆ isapplied to the port 6, voltages V_(A) and V_(B) at nodes A and B at bothends of resistor Rx are

$\begin{matrix}{V_{A} = {V_{B} + {I_{2}{Rx}}}} \\{= {{V_{B}\lbrack {Z_{2} + {Rx} + {( {\alpha - 1} ){Rx}}} \rbrack}/\lbrack {Z_{2} + {( {\alpha - 1} ){Rx}}} \rbrack}} \\{= {{V_{B}\lbrack {Z_{2} + {\alpha \; {Rx}}} \rbrack}/\lbrack {Z_{2} + {( {\alpha - 1} ){Rx}}} \rbrack}}\end{matrix}$ V_(B) = I₂[Z₂ + (α − 1)Rx/2]

Moreover, voltage V₃ at the port 3 and voltage V₄ at the port 4 arerespectively expressed as

$\begin{matrix}{V_{3} = {MVr}} \\{= {M( {V_{A} - V_{B}} )}} \\{= {V_{A}{{MRx}/( {Z_{2} + {Rx} + {( {\alpha - 1} ){Rx}}} )}}} \\{= {V_{A}{{MRx}/( {Z_{2} + {\alpha \; {Rx}}} )}}}\end{matrix}$ V₄ = V_(B).

Hence, the passing characteristics from the port 6 to the ports 3 and 4are derived as

S[3,6]=V ₃ /V ₆ =V _(A) MRx/{V ₆(Z ₂ +αRx)}

S[4,6]=V ₄ /V ₆ =[Z ₂+(α−1)Rx]V _(A) /[VV ₆(Z ₂ +αRx)].

Through a similar discussion, assuming that current I₁ flows through thecircuit Z₁ when voltage V₅ is applied to the port 5, voltages V_(A) andV_(B) at the nodes A and B at both ends of resistor Rx are respectivelyexpressed as

V_(A) = I₁(Z¹⁻α Rx) $\begin{matrix}{V_{B} = {V_{A} + {I_{1}{Rx}}}} \\{= {{V_{A}( {Z_{1} - {\alpha \; {Rx}} + {Rx}} )}/( {Z_{1} - {\alpha \; {Rx}}} )}} \\{= {{V_{A}\lbrack {Z_{1} + {( {1 - \alpha} ){Rx}}} )}/{( {Z_{1} - {\alpha \; {Rx}}} ).}}}\end{matrix}$

Also, the voltage V₃ at the port 3 and the voltage V₄ at the port 4 arerespectively expressed as

$\begin{matrix}{V_{3} = {MVr}} \\{= {M( {V_{B} - V_{A}} )}} \\{= {{- V_{B}}{{MRx}/( {Z_{1} - {\alpha \; {Rx}} + {Rx}} )}}} \\{= {{- V_{B}}{MR}\; {x/\lbrack {Z_{1} + {( {1 - \alpha} )\; {Rx}}} \rbrack}}}\end{matrix}$ V₄ = V_(B).

Therefore, the passing characteristics from the port 5 to the ports 3and 4 are derived as

S[3,6]=V ₃ /V ₅ =−V _(B) MRx/[V ₅ {Z ₁+(1−α)Rx}]

S[4,5]=V ₄ /V ₅ =V _(B) /V ₅.

As a result,

S[4/6]/S[3,6]=[Z ₂+(α−1)Rx]/(MRx)

S[4/5]/S[3,5]=−[Z ₁+(1−α)Rx]/(MRx).

Here, by selecting MRx=1, it is proved that the circuit impedances Z₁and Z₂ are obtained as

Z ₁ =−S[4,5]/S[3,5]−(1−α)Rx

Z ₂ =S[4,6]/S[3,6]+(1−α)Rx.

As above, it is proved that the circuit impedances Z₁ and Z₂ areobtained from the passing characteristics from the ports 5 and 6 to theports 3 and 4. Hence, viewing the circuit side, the forward and backwardreflection coefficients Γ_(S) and Γ_(L) are obtained respectively as

Γ_(S)=(Z ₁ −Z ₀)/(Z ₁ +Z ₀)

Γ_(L)=(Z ₂ −Z ₀)/(Z ₂ +Z ₀).

Here, Z₀ is system impedance and inner resistance of the S parameterprobe and is ordinarily 50 Ω.

In the actual calculation for the small-signal analysis on a circuitsimulator, the circuit reflection coefficients are calculated directlyfrom circuit topologies; a process to observe an output response inreply to the probe signal input is not employed. However, atlarge-signal analysis, the process described above is employed; byobserving an output response in reply to the probe signal input, thecircuit impedances Z₁ and Z₂ are obtained from the passingcharacteristics from the ports 5 and 6 to the ports 3 and 4. Assumingthat when a voltage V6 is applied to the port 6, voltages V36 and V45appear respectively at the ports 3 and 4, and when a voltage V5 isapplied to the port 5, voltages V35 and V36 appear respectively at theports 3 and 4, the circuit impedances Z₁ and Z₂ are represented as

Z ₁ =−V45/V ₃₅−(1−α)Rx

Z ₂ =V46/V36+(1−α)Rx.

Typical values of the resistors Rs and Rx and the parameter M of thepower source to be actually employed are favorably set, for example, as

Rs=10 MΩ

Rx=1 Ω

M=1

α=½.

FIG. 3 shows the no-loss S-probe when these typical circuit parametersare employed in the configuration.

In this connection, there also exists a circuit simulator in which aresistance value having a minus value (i.e., a negative resistancevalue) cannot be employed as the input circuit parameter. In such case,to obtain a general resistance −αRx which is expanded to include anegative resistance value in general, it is only required to set, in a4-parameter admittance matrix element {Y} shown on the right side ofFIG. 2, as

Y[1,1]=−1/αRx, Y[1,2]=1/αRx

Y[2,1]=1/αRx, Y[2,2]=−1/αRx;

to obtain, for example, the negative resistance −Rx/2, it is onlynecessary to set

Y[1,2]=−2/Rx, Y[1,2]=2/Rx

Y[2,1]=2/Rx, Y[2,2]=−2/Rx

as shown on the right side of FIG. 3.

The S-probe is a 6-port circuit; hence, in the procedure for the circuitoscillation analysis and design, when n S-probes are used, there isconducted multi-port analysis for about 6n ports; and in thelarge-signal analysis, a two-tone harmonic balance analysis is required;hence the analysis becomes considerably complex.

EXEMPLARY EMBODIMENT 2

Description will now be given of an example in which the method of theno-loss S-probe is applied to an oscillator circuit design as the basisof the microwave circuit oscillation analysis and design. FIG. 4 is abasic circuit layout diagram of an oscillator to be described here. AnFET is used as an active element and a series feedback form in which asource terminal has a stub is employed in the circuit configuration. Asshown in the diagram, the S-probe is inserted in the gate terminal andthe drain terminal of the oscillator to obtain the reflectioncoefficients toward the left and the right of the circuit therefrom. Inthe circuit configuration of this type, since an oscillation signal isordinarily outputted from the drain side and the load is coupled withthe drain side, the oscillation condition is judged by the reflectioncoefficient (characteristic impedance) at the drain terminal.

Assume that when viewing the active element side and the load side, thereflection coefficients are respectively Γ_(S1) and Γ_(L1), as shown inFIG. 4. The oscillation start condition is determined by the reflectioncoefficients in the small-signal state; namely, for oscillation startangular frequency ω,

abs(Γ_(S1)Γ_(L1))>1 and

phase(Γ_(S1))+phase(Γ_(L1))=0.

This is equivalent to the oscillation start condition when thecharacteristic impedances obtained by viewing the active element sideand the load element side are set as Z_(out) and Z_(L), namely,

Re{Z _(out)(ω)}<0 and |Re{Z _(out)(ω)}|>Re{Z _(L)(ω)}

IM{Z _(out)(ω)}+Im{Z _(L)(ω)}=0,

but it is more simply expressed.

Moreover, the oscillation continuation condition is determined by thereflection coefficients in the oscillation stationary state(large-signal state); for an oscillation stationary state angularfrequency ω₀,

abs(Γ_(S1)Γ_(L1))=1   (B1)

phase(Γ_(S1))+phase(Γ_(L1))=0   (B2).

This is equivalent to the oscillation start condition when thecharacteristic impedances obtained by viewing the active element sideand the load element side are set as Z_(out) and Z_(L), namely,

Re{Z _(out)(ω₀)}<0 and |Re{Z _(out)(ω₀)}|=Re{Z _(L)(ω₀)}

Im{Z _(out)(ω₀)}+Im{Z _(L)(ω₀)}=0,

but it is more simply expressed.

On the microwave circuit CAD software ADS of Agilent Technology, aspecific circuit design is conducted for an oscillator. This is anexample of the designing of a millimeter-wave oscillator (to be referredto as 60 GHz-OSC hereinbelow) for the 60 GHz band. As an equivalentcircuit of an FET, a Curtis cubic model is used for simplicity.

FIG. 5( a) and (b) illustrate a design (small signal) of the oscillationstart based on the above oscillation condition in a specific oscillatorcircuit. FIG. 5( a) shows a plotted result of the reflection coefficientat the gate terminal of the oscillator versus the frequency, and FIG. 5(b) shows a plotted result of the reflection coefficient at the drainterminal. It can be understood that the S-probe causes no perturbationin the circuit (in particular, strictly no perturbation at small signalanalysis); hence, for both of (a) and (b), the oscillation startcondition is satisfied at one and the same frequency (about 62 GHz)according to the oscillation theory.

FIG. 6 shows occurrence of negative resistance and a relation thereof tothe oscillation start in the 60 GHz-OSC. In the diagram, Zd is acharacteristic impedance obtained when viewing the active element sidefrom the S-probe at the drain terminal. The real part of Zd in FIG. 6indicates occurrence of negative resistance equal to or more than 50 Ωin a range from about 45 GHz to about 65 GHz. In addition, the imaginarypart of Zd has a clear change point from “capacitive” to “inductive”near 62 GHz, and the change point is in the frequency band in which thenegative resistance is taking place. That is, the change point indicatesa frequency to cause oscillation; as for the small signal, it is alsoimplied that this oscillator is capable of conducting stableoscillation.

Description has been given of an example of analysis using a smallsignal in a situation in which oscillation is about to start. However,in the stationary state, the oscillator is in the large-signal state;hence, the reflection coefficient in this state is required to becalculated in the large-signal state. In the large-signal analysis, inaddition to the basic tone to conduct the oscillation harmonic balancesimulation, a probing large signal to sweep the frequency is applied asthe second tone to the S-probe to obtain the reflection characteristic;hence, a two-tone harmonic balance analysis is conducted. When theno-loss S-probe is employed, it is not necessary to employ an extremelysmall value for Rx of FIG. 2 due to the assist of the negativeresistance. Therefore, at large-signal analysis, it is only required toapply as the probe signal a signal of relatively small power whichhardly causes perturbation in the circuit; and it is possible to obtainthe reflection coefficient (impedance) in the large-signal state almostwithout perturbation (namely, correctly). In the relevant method, sinceit is required to apply a relatively large probe signal, perturbationoccurs in the circuit; hence, the correct circuit characteristic cannotbe obtained according to the principle of active load pull.

FIG. 7 shows the reflection coefficient at the drain terminal atstationary oscillation of the 60 GHz-OSC in the above 2-tone harmonicbalance method. The 60 GHz-OSC of this report oscillates at 59.88 GHz onthe simulation and oscillation power is 13.2 dBm. In the 2-toneanalysis, in addition to the basic tone, a probing large signal of −30dBm is applied via the S-probe to the circuit to obtain the reflectioncoefficient for each frequency by sweeping the frequency. It isrecognizable that the reflection coefficient characteristic and thephase characteristic of FIG. 7 satisfy expressions (B1) and (B2), whichare to be satisfied by the oscillation stationary state at 60 GHz,according to the oscillation theory. This is one of the examplesindicating that the method in which the reflection coefficient(characteristic impedance) at an arbitrary point of the circuit iscalculated by use of the no-loss S-probe of this report is alsoeffective to the large-signal state. The method of applying it to anamplifier is basically similar to that of applying it to the oscillator.

The proposed no-loss S-probe on the circuit simulator can correctlyobtain the reflection coefficients (impedances) at an arbitrary point ofa circuit toward the left-hand section and the right-hand section of thecircuit even in the large-signal state by using the negative resistance.Hence, it can be considered that the no-loss S-probe contributes todevelopment of the oscillator design and to detection and suppression ofparasitic oscillation of the amplifier. For the exemplary embodiment 1,description has been first given of the principle of the no-loss P-probemethod; additionally, for the exemplary embodiment 2, description hasbeen given of an example in which the present invention is applied tothe oscillator circuit design which is the basis of the oscillationanalysis and design of the microwave circuit. Application to theamplifier will be described in conjunction with an exemplary embodiment3 and a subsequent exemplary embodiment.

EXEMPLARY EMBODIMENT 3

If a microwave amplifier is simply designed to have a gain in a band inwhich signals are to be amplified, the amplifier has an unnecessary gainoutside the band in some cases. Particularly, in a situation wherein amillimeter-wave transistor is adopted as an active element, since thistransistor has a gain in a range up to a high frequency of themillimeter wave band, it naturally has a larger gain for less frequency;hence, the millimeter-wave transistor has an unnecessary gain outsidethe band. If such unnecessary gain outside the band satisfies theoscillation condition, a parasitic oscillation takes place.

It is known that the amplifier parasitic oscillation is generallyclassified into even-mode oscillation and odd-mode oscillation (looposcillation). The even mode oscillation is oscillation judged by astability factor K. On the other hand, the odd-mode oscillation isoscillation which occurs when components connected in parallel to eachother in a circuit are driven with mutually opposite phases and cannotbe judged by the stability factors K or MU-value which is often used ingeneral.

To detect danger of the odd-mode oscillation (loop oscillation) on acircuit simulator, there has been often employed a method in which aparticular loop is severed from the overall circuit and the odd-modeoscillation is detected by a loop gain when a probe signal is injectedby use of a circulator. However, since it is required in suchconventional method to sever the particular loop of the circuit toconduct the analysis, there exists a drawback that the inherentcharacteristic of the overall circuit cannot be obtained. Therefore,when compared with the detection of the even-mode oscillation, thedetection of the odd-mode oscillation is less quantitative, which makesit difficult to detect (or to suppress) parasitic oscillation in theamplifier.

Here, description will be given of a method for relatively simply andcorrectly detecting not only the even-mode oscillation, but also theodd-mode oscillation of the amplifier on a circuit simulator by usingthe proposed no-loss S-probe (FIG. 2 or 3); further, experimental valuesare compared with calculated values. In the present method, it ispossible, without severing the particular loop of the circuit, tocalculate the reflection coefficient (characteristic impedance) in thesmall-signal state and the large-signal state by inserting theno-perturbation S-probe in the circuit, i.e., in a cross section of thecircuit. Hence, it is recognized that when compared with relevantmethods, the even-mode parasitic oscillation and odd-mode parasiticoscillation can be more correctly detected. Moreover, by judgingstability using the present method together with the relevantstabilization factors such as the K-value and the MU-value, stability ofthe amplifier can be more precisely designed. Also, stability of eachstage of a multistage amplifier can be individually and quantitativelyknown.

(3-1. Amplifier Stability Analysis by S-probe Method)

FIG. 8 is a circuit diagram in which the no-perturbation S-probe isapplied to the stability analysis for a multistage amplifier. Todetermine stability of a circuit component by the S-probe, the S-probeis inserted in a configuration in which the circuit component issandwiched by the S-probe as shown in the diagram. The method ofobtaining the reflection coefficient in a circuit cross section is basedon the method described in detail in conjunction with the exemplaryembodiment 1.

In general, to make an i-th stage amplifier stable,

abs{Γ _(S(i−1))*Γ_(L(i−1))}<1 and abs(Γ_(Si)*Γ_(Li))<1   (C1)

is required. (Since the active element is actually not unilateral, onlyeither one the former and latter expressions may also be ordinarily usedfor the two expressions). The condition required to make the overallcircuit of an n-stage amplifier stable is, since each stage is requiredto be stable in general,

abs(Γ_(S0)*Γ_(L0))<1

and

abs(Γ_(S1)*Γ_(L1))<1

. . .

and

abs(Γ_(Sn)*Γ_(Ln))<1   (C2)

These form a condition more severe than that of the expression of thetype of

Real(Γ_(Si)*Γ_(Li))<1   (C3)

of the original paper [1] of Wang et al; however, since there takesplace an inconsistency wherein even if expression (C3) is satisfied,there exists a case in which an oscillation condition is satisfiedaccording to the oscillation theory; this report hence adopts, as thestability judging formula, expression (C1) or (C2) which is faithful tothe oscillation theory.

Contrarily, to make the i-th amplifier oscillate, the conditionalexpressions

abs(Γ_(S1)*Γ_(L1))>1   (C4)

phase(Γ_(S1))+phase(Γ_(Li))=0   (C5)

are satisfied.

As above, in the present method, it is possible, without severing theparticular loop of the circuit and without inserting a circulatortherein, to calculate the reflection coefficient (characteristicimpedance) in the small-signal state and the large-signal state byinserting the no-perturbation S-probe in the circuit, i.e., in a crosssection of the circuit. Hence, when compared with the relevant methods,the even-mode parasitic oscillation and odd-mode parasitic oscillationcan be more correctly detected. Also, stability of each stage of amultistage amplifier can be individually and quantitatively knownaccording to expression (C1).

Hereinbelow, description will be given of an example of analysis for theeven-mode oscillation and the odd-mode oscillation in a specificamplifier. First, description will be given of a method of detecting theeven-mode oscillation through a small-signal analysis. Next, thedetection and suppression of the odd-mode oscillation by use of a smallsignal will be discussed and then the stability is further examinedthrough a large-signal analysis; finally, for the odd-mode oscillation,experimental values are compared with calculated values.

(3-2. On Even-Mode Oscillation in Amplifier)

Consider here, as a specific example of an amplifier, a V-bandmillimeter wave amplifier constructed by an active element in which FETshaving a gate width Wg=400 μm are connected in parallel to each other byuse of gate and drain lead lines (FIG. 9 shows an equivalent circuit;this will be abbreviated as 60 GHz-AMP hereinbelow). As the FET, thereis adopted a heterojunction FET (HJFET) of double-dopeddouble-heterostructure with gate length Lg=0.15 μm, gate width Wg=400μm, and a gate-metallized TiAlTi AlGaAs/InGaAs/AlGaAs channel. As thegate lead line, a phase-restoring capacitor is formed for impedancematching. An equivalent circuit model of the FET employed for thecalculation is constructed on the basis of measurement results ofcharacteristics of an FET actually manufactured as a trial productthrough mass production processes for millimeter wave devices. As a biascircuit, an RC bias network is applied.

FIG. 10 shows a small-signal characteristic of the amplifier of FIG. 9on the simulation. It is recognized that at 60 GHz, there are obtainedfavorable input and output impedance matching and a gain of 8 dB (Vd=4V, A-class operation). FIG. 11 shows plotting of the stabilizationfactor K-value. The K-value shows, near 30 GHz, a low value about one,but the value is one or more for other frequencies; as far as it is seenfrom the drawing, the circuit stability seems to be almost secured.

Further, FIG. 12 shows a result of stability judgment based onexpression (C1) or expressions (C4) and (C5). In this case, the S-probeis inserted in a location outside the loop circuit section of the FETsconnected in parallel to each other and there exists no closed loopcircuit section configured via the S-probe; hence, the detection ofeven-mode oscillation is carried out. In FIG. 12, for the absolute valueof the reflection coefficient as well as for the phase, the oscillationcondition is not satisfied; hence, for the even-mode excitation, nodanger of oscillation exists for the circuit, which is hence stable.

(3-3. On Odd-Mode Oscillation in Amplifier)

The even-mode oscillation of the 60 GHz-AMP has been discussed above;here, the odd-mode oscillation will be discussed.

As an amplifier to be discussed, a 60 GHz-AMP, which is completely equalto FIGS. 8 and 9 excepting the balanced resistor, will be employed as anexample. To detect the odd-mode oscillation, the S-probe is inserted ina closed loop section of the circuit in which odd-mode oscillationlikely occurs as shown in an equivalent circuit of FIG. 13.

The small-signal characteristic and the stability factor K-value of thisamplifier are completely equal to those shown respectively in FIGS. 10and 11 regardless of presence or absence of the balanced resistor.

FIG. 14 shows the stability factor according to expression (C1) orexpressions (C4) and (C5) at the drain terminal by use of the S-probewhen the balanced resistor is not applied. It can be seen that near 30GHz, the conditions of the reflection coefficient and the phase almostsatisfy the oscillation condition, and the 60 GHz-AMP is unstable near30 GHz. To further check more precisely, the characteristic impedance Zdviewed from the drain terminal to the active element side is shown inFIG. 15. According to FIG. 15, it is recognized that the 60 GHz-AMP isnot only unstable near 30 GHz, but also satisfies the oscillationcondition, and has a danger to cause the odd-mode oscillation.

Additionally, FIG. 16 shows stability of the 60 GHz-AMP for the odd-modeoscillation when the balanced resistor 15 Ω is applied. As can be seenfrom FIG. 16, it is known that as far as the small-signal levelconcerns, the odd-mode oscillation is suppressed by the balancedresistor.

Further, an optimization design of the balanced resistor value isconducted using the 60 GHz-AMP. FIG. 17 is a graph in which the maximumvalue of abs(Γ_(S1)*Γ_(L1))=abs(Gamma_S1*Gamma_L1) near 30 GHz isemployed as the oscillation index and is plotted with respect toconductance of the balanced resistor. In this situation, the balancedresistor appropriately ranges from 15 Ω to 40 Ω, and 25 Ω is selected asan optimal value.

Incidentally, the discussion up to now is associated with the stabilityanalysis in the small-signal state; FIG. 18 compares the reflectioncoefficient for each frequency in amplifier operation of the 60 GHz-AMPusing a large-signal input with that in the small-signal operation. Thecalculation of the reflection coefficient for the large-signal input isa 2-tone harmonic balance analysis. It is assumed in the 2-tone analysisthat the input large signal to the amplifier 60 GHz-AMP has a basic toneof 60 GHz and 15 dBm and the second-tone probe signal to be inputted tothe S-probe by sweeping the frequency is −30 dBm. The 60 GHz-AMP isstable for the odd-mode excitation in the small-signal operation byconnecting the balanced resistor of 25 Ω as shown in FIG. 18; however,with the large-signal input of 15 dBm, it shows a characteristic ofunstableness at about 30 GHz (Vd=4 V, A-class operation). Further, byalso calculating the phase characteristic, it can be seen that thisamplifier is not only stable for the odd-mode excitation near 30 GHz,but also satisfies the oscillation condition as shown in FIG. 19. Itwill be considered that the odd-mode unstableness in the large-signalstate detected on the circuit simulator in the no-loss S-probe method asabove corresponds to “band break phenomenon” (a phenomenon in which acircuit showing a stable operation with a small signal becomes unstablewhen a large signal having a certain level is inputted, and showsparasitic oscillation) often seen in experiments of power amplifieroperation.

Thereafter, by use of an actual amplifier, observed frequency values ofparasitic oscillation, which is regarded as odd-mode oscillation, aresimply compared with large-signal calculation values using the presentmethod under one and the same condition in Table 1 (descriptionregarding details of specifications, operation conditions, and the likeof the amplifier will be omitted here).

TABLE 1 Experimental values Calculated values V-band amplifier 32.178GHz 30.0 GHz C-band amplifier 1.514 1.4 3.104 3.2 7.041 6.9

In Table 1, the amplifier shows a stability factor K of one or more forall frequencies with the operation bias; although the operation isstable with a small signal, parasitic oscillation is shown when a largesignal of a certain level is inputted in an ordinary operation. It canbe hence considered that the parasitic oscillation of Table 1 isodd-mode oscillation (loop oscillation). It can be seen in this examplethat the method of this report is capable of also relativelyquantitatively predicting and detecting parasitic oscillation. For theparasitic oscillation of the amplifier in Table 1, experimentally and inthe calculation, there regrettably exist both cases in which theparasitic oscillation is suppressed or not suppressed by the applicationof the balanced resistor. For a further quantitative oscillationanalysis using a large-signal analysis, it is required to employ ahighly accurate model as the large-signal model of the active element(e.g., the EEHEMT model configured by use of ICCAP of Agilent).

In this section, description has been given of the detection of odd-modeoscillation concentrating on the outlining of the method. Due to thepresent method, without severing a particular loop of the circuit, thereflection coefficient (impedance) can be calculated for small-signaland large-signal operations by inserting the S-probe in a cross sectionof the circuit. As a result, when compared with relevant methods, theeven-mode parasitic oscillation and the odd-mode parasitic oscillationcan be more correctly detected. However, the stability factors relatedto the K-value and the MU-value still remain as strong means to analyzestability regarding the even-mode excitation of the entire circuit.Hence, by using the stability analysis according to the present methodtogether with these method, it can be considered that the stabilitydesign of the amplifier can be more precisely realized.

EXEMPLARY EMBODIMENT 4

To obtain high power from an amplifier, it is required to flow a largecurrent through the transistor as the active element. Increasing thecurrent flowing through the transistor is achieved by conducting anoptimal design of the active layer and by operating a plurality oftransistors in a parallel configuration.

However, if the transistors are simply arranged by use of lead lines ina parallel configuration as an active element, odd-mode oscillation(loop oscillation) may be caused depending on cases. In a situationwherein the odd-mode oscillation occurs, there is at present noeffective measure to securely suppress the odd-mode oscillation. Anothermethod to obtain high power is arranging unitary amplifiers in aparallel configuration by use of a power distributing and coupling unitand a hybrid. However, also in this case, it cannot be considered thatthere exists no danger of odd-mode oscillation depending on the parallelconfiguration method.

In this report, description will be first given of a systematic methodin which to check circuit stability when a parallel-type amplifier isconstructed, the stability is known from the reflection coefficient(characteristic impedances) of a circuit cross section by use of theproposed no-loss S-probe. Next, for the stability of theparallel-configuration amplifier, particularly, resistivity against theodd-mode excitation, the difference thereof will be compared accordingto the types of power distributing and coupling units and hybridsemployed.

(4-1. Systematic Method of Checking Stability of Parallel-TypeAmplifier)

Stability of a circuit can be judged, according to the oscillationtheory, by obtaining the reflection coefficients in the forwarddirection and the backward direction in an arbitrary cross section ofthe circuit. To obtain the reflection coefficients in the cross sectionof the circuit, it is convenient to adopt the proposed no-loss S-probewhich causes no loss even if it is inserted in the circuit and which isavailable in small-signal and large-signal operations.

To make the circuit stable, it is required that

abs(Γ_(S)*Γ_(L))<1   (D1)

holds at any virtual cross-sectional point of the circuit. Additionally,to make the circuit be about to oscillate, it is required that

abs(Γ_(S)*Γ_(L))>1   (D2)

and

phase(Γ_(S))+phase(Γ_(L))=0   (D3)

hold at a virtual cross-sectional point in the small-signal state. Inthe stationary oscillation state in which the circuit oscillatescontinuously,

abs(Γ_(S)*Γ_(L))=1   (D4)

and

phase(Γ_(S))+phase(Γ_(L))32 0   (D5)

hold at any virtual cross-sectional point in the large-signal state. Ifthe stability condition of expression (D1) is not satisfied as well asthe stability conditions of expressions (D2) and (D3) are not satisfiedat a virtual cross-sectional point in the circuit, the circuit does notoscillate or the circuit oscillates, but does not conduct stableoscillation in many cases.

Circuit stability of the parallel-type amplifier can be checked byapplying the above method. FIG. 20 shows structure of a circuit forchecking stability in the parallel-type amplifier. Ordinarily, thesignal attenuation quantity of the attenuator is set to zero. In FIG.20, if the oscillation condition is satisfied in S-probe 1 (or 1′),even-mode parasitic oscillation occurs in the circuit. Therefore, inthis case, the oscillation condition is ordinarily satisfied in probe 2(or 2′). On the other hand, in a situation wherein the oscillationcondition is satisfied in the probe 2 (or 2′) in the closed-loopcircuit, but unstableness is not observed in the probe 1 (or 1′) outsidethe loop; odd-mode parasitic oscillation (loop oscillation) occurs inthe circuit. In a case wherein when even-mode parasitic oscillationoccurs and odd-mode oscillation concurrently occurs in the closed loop,if the signal attenuation quantity is increased by the attenuator inFIG. 20, the oscillation is stopped in the probe 1 (or 1′), but theoscillation condition is continuously observed in the probe 2 (or 2′) inthe closed loop; in this way, the concurrent occurrence of odd-modeoscillation can be checked.

The method in which the circuit stability is judged by calculating thereflection coefficient in a virtual cross section of the circuit asabove is quite a clear method according to the oscillation theory since,for example, whether the parasitic oscillation is due to even-modeexcitation or odd-mode excitation is easily judged.

In the oscillation analysis of an oscillator, the probe to calculate thereflection coefficient is ordinarily inserted in an output side of theactive element (ordinarily, in the drain terminal for an FET). On theother hand, in the parasitic oscillation analysis of an oscillator, ifthe probe to calculate the reflection coefficient is inserted in aninput side of the active element (ordinarily, in the gate terminal foran FET), it is likely to detect unstableness in many cases. This isbecause in the case of an amplifier, a reflection wave from the activeelement caused due to difficulty in establishing input matching remainsas a standing wave in the closed loop formed in the circuit and becomesthe primary cause to induce odd-mode oscillation (loop oscillation).

(4.2. Contribution of Various Power Distributing and Coupling Units andHybrids to Circuit Stability)

In general, a method of power-coupling unitary amplifiers for which ithas been confirmed that neither even-mode parasitic oscillation norodd-mode parasitic oscillation occurs therein for power-coupling by useof a power distributing and coupling unit and a hybrid is regarded as aneffective method to double the power from the amplifier while keepingthe circuit stability secured. This is because the power distributingand coupling unit and the hybrid have a function to distribute and tocouple power in an operation band as well as a function to cutunnecessary signals outside the band; also, the Wilkinson powerdistributing and coupling unit or the like has also a function toisolate ports for signal coupling and distribution. It has beenexperimentally known that the feared loss in the power distributing andcoupling can be simply reduced by devising the manufacturing of thepower distributing and coupling unit such that the manufacturing iscarried out according to designed values as strictly as possible; hence,it will not be a problem.

However, it does not mean that every power distributing and couplingunit or hybrid can carry out some effect of the power coupling operationand the circuit stabilization. Accordingly, a method of selecting acircuit configuration by use of the method described above will bediscussed hereinbelow in which difference in the stability of theparallel-structure amplifier, particularly, in the resistivity againstthe odd-mode excitation due to the kinds of the power distributing andcoupling unit and the hybrid is compared to select a circuitconfiguration most favorable to the power coupling in accordance witheach purpose.

First, as an example of a specific amplifier corresponding to theunitary amplifier of FIG. 20, let us consider a 60 GHz-band millimeterwave amplifier including FET as an active element which has a gate widthof Wg=400 μm (to be abbreviated as 60 GU-AMP hereinbelow). As the FET,there is adopted a heterojunction FET (HJFET) which has gate lengthLg=0.15 μm and double-doped double-heterostructure with agate-metallized TiAlTi AlGaAs/InGaAs/AlGaAs channel. As the gate leadline, a phase-restoring capacitor is formed for impedance matching. AnRC bias network is applied to the bias circuit.

FIG. 21 shows the small-signal characteristic of the amplifier of thetrial product (S parameter of an amplifier prepared by re-configuring asmall-signal FET equivalent circuit model configured to faithfullyreproduce the measured S parameter; S-parameter not actually measured isalso calculated for frequencies equal to or more than 80 GHz). It isrecognized that favorable input/output impedance matching is attained at60 GHz and a gain of 5.5 dB is obtained (Vd=4 V, A-class operation).

FIG. 22 shows plotting of the stability factor K-value. The K-valueshows a low value of about one at a little less than 30 GHz and is equalto or more than one for the other frequencies, and stability against theeven-mode excitation is secured. Also, in this trial product, noparasitic oscillation is observed in an actual evaluation; it can behence considered that stability against the odd-mode excitation is alsosecured. Further, in a power evaluation for the 60 GHz band, Psat=21.0dBm is obtained.

Next, the circuit stability of a parallel amplifier which has thecircuit configuration of FIG. 20 and which aims to double the power inthe 60 GHz band by employing the amplifier 60 GU-AMP of FIG. 21 as theunitary amplifier is examined.

(4-2-1. Power Distributing and Coupling by Y-branch)

First, an amplifier of FIG. 23 in which 60 GU-AMP are arranged in aparallel configuration by using a Y-branch (or a T-branch) includingonly simple wiring is considered. For the Y-branch and wiring sections,models constructed on the ADS are employed.

FIG. 24 shows the small-signal characteristic of a Y-branch parallelamplifier. Since there exists input/output impedance mismatching due tothe Y-branch, deterioration in the matching level is seen on the inputside and a shift in the matching frequency is seen on the output side.

FIG. 25 shows the stability factor K of the Y-branch parallel amplifier.Near 25 GHz, the K-value is about one, but the stability factor Kindicates a value equal to or more than one for all frequencies rangingfrom DC to 100 GHz; it is hence known that this amplifier is stable forthe even-mode excitation.

FIG. 26 shows the stability for the odd-mode excitation of the Y-branchparallel amplifier based on expressions (D2) and (D3) by use of theS-probe inserted in the circuit as shown in FIG. 9. Along the leftY-axis, the stability factor (D2) for the reflection coefficient isplotted; and along the right Y-axis, the phase condition (D3) isplotted. As can be seen from this graph, it is recognizable that theoscillation start condition is satisfied at about 75 GHz in thisamplifier and there exits danger of occurrence of odd-mode parasiticoscillation. The Y-branch has merits of the smallest circuit size andsimple structure, but has not the isolation function betweendistributing (or coupling) ports; hence attention is to be given to thatthe odd-mode parasitic oscillation easily occurs in the Y-branch powerdistributing and coupling parallel amplifier as above. However, theremay be considered a scheme wherein when wiring loss and Y-branch lossare relatively large, the circuit is turned to be stabilized by usingthe loss.

(4-2-2. Wilkinson In-phase Power Distribution and Coupling)

Next, an amplifier shown in FIG. 27 in which 60 GU-AMP are arranged in aparallel configuration using the Wilkinson power distributing andcoupling unit is considered. For the 60 GHz-band Wilkinson powerdistributing and coupling unit and wiring sections, models constructedon ADS are used. FIG. 28 shows the small-signal characteristic of theWilkinson-type parallel amplifier. A favorable matching characteristicis shown for both of the input and output sides. FIG. 29 shows thestability factor K of the Wilkinson-type parallel amplifier. For allfrequencies ranging from DC to 100 GHz, the stability factor K is morethan one; it is hence recognizable that this amplifier is stable for theeven-mode excitation.

FIG. 30 shows the stability for the odd-mode excitation of theWilkinson-type parallel amplifier based on expressions (D2) and (D3) byuse of the S-probe inserted in the circuit as shown in FIG. 27. Thestability factor (D2) calculated from the reflection coefficient issufficiently reduced to a value less than one in a wide band rangingfrom DC to 100 GHz; it can be hence recognized that this amplifier isfully stable for the odd-mode excitation. As above, in the Wilkinsonpower distribution and coupling unit, the isolation resistor has anisolation function not only for signals within the band, but also forsignals with wider frequencies outside the band; hence, it can beconsidered that the amplifier constructed in the parallel structure byuse of the Wilkinson power distribution and coupling unit has highstability in a wide band for the odd-mode excitation.

(4-2-3. Balance-Type Power Distribution and Coupling by 90-degreeHybrid)

Next, an amplifier shown in FIG. 31 in which 60 GU-AMP are disposed in aparallel configuration using a 90-degree hybrid is considered. In thiscase, a branch line coupler of 60 GHz-band operation is selected as the90-degree hybrid. For the branch line coupler and wiring sections,models constructed on ADS are used. FIG. 32 shows the small-signalcharacteristic of the 90-degree hybrid balance-type amplifier. Quite afavorable matching characteristic is shown in a sufficiently wide bandfor both of the input and output sides. In general, for the balance-typeamplifier using the 90-degree hybrid, reflection power from each unitaryamplifier to the input and output ports is entirely absorbed by thehybrid termination resistor within the band; the amplifier hence has anadvantage in which even if the input/output impedance of the unitaryamplifier differs from the route impedance Zo (ordinarily 50 Ω), itseems as if the input/output impedance of the balance-type amplifier iskept at Zo. Hence, for an amplifier for which the input/output matchingis not easily established, the input/output matching is facilitated forthe amplifier by employing the configuration of the balance-typeamplifier. FIG. 33 shows the stability factor K of the 90-degree hybridbalance-type amplifier. The stability factor K is more than one for allfrequencies ranging from DC to 100 GHz, and it is hence recognized thatthis amplifier is stable for the even-mode excitation.

FIG. 34 shows the stability for the odd-mode excitation of the 90-degreehybrid balance-type amplifier based on expressions (D2) and (D3) by useof the S-probe inserted in the circuit as shown in FIG. 31. Thestability factor (D2) calculated from the reflection coefficient is lessthan one in a wide band ranging from DC to 100 GHz; it is hencerecognizable that this amplifier is fully stable for the odd-modeexcitation. However, near 25 GHz, the stability factor (D2) according tothe reflection coefficient is in the vicinity of one, and an unnecessarygain is attained also in FIG. 32; hence, it cannot be asserted thatsufficient stability is secured in the large-signal input operation. Asabove, for the balance-type amplifier employing the 90-degree hybrid,reflection power from each unitary amplifier between the distribution(or coupling) ports is not fully isolated outside the band of thehybrid; therefore, the amplifier cannot be considered to be sufficientwith respect to the stability for the odd-mode excitation.

(4-2-4. Push-Pull Power Distribution and Coupling by 180-Degree Hybrid)

Next, a push-pull amplifier shown in FIG. 35 in which 60 GU-AMP aredisposed in a parallel configuration by use of a 180-degree hybrid isconsidered. The push-pull amplifier generally has a merit in whichhigher harmonics of even-numbered degrees cancel out in the output wave.Here, a rat-race hybrid of 60 GHz-band operation is selected as the180-degree hybrid. For the rat-race hybrid and wiring sections, modelsconstructed on ADS are adopted. FIG. 36 shows the small-signalcharacteristic of the 180-degree hybrid push-pull amplifier. A favorablematching characteristic is shown for both of the input and output sides.FIG. 37 shows the stability factor K of the 180-degree hybrid push-pullamplifier. The stability factor K is more than one for all frequenciesranging from DC to 100 GHz, and it can be hence recognized that thisamplifier is stable for the even-mode excitation.

FIG. 38 shows the stability for the odd-mode excitation of the180-degree hybrid push-pull amplifier based on expressions (D2) and (D3)by use of the S-probe inserted in the circuit as shown in FIG. 34. Thestability factor (D2) calculated from the reflection coefficient is lessthan one in a wide band ranging from DC to 100 GHz; it is hencerecognizable that this amplifier is stable for the odd-mode excitation.However, judging simply, the stability factor according to thereflection coefficient is in the vicinity of one for frequencies near 25GHz; hence, it cannot be simply asserted that this amplifier, like the90-degree hybrid balance-type amplifier, is fully stable in thelarge-signal operation. The evaluation of FIG. 38 is obtained by using arat-race hybrid in which a certain degree of isolation is providedbetween the distribution (or coupling) ports is employed as the180-degree hybrid. In a situation wherein a Marchand balun is used asthe 180-degree hybrid, although there exists a merit that the phaseshift quantity is kept at 180 degrees in the wide band as compared withthe rat-race hybrid, the isolation between the distribution (orcoupling) ports is insufficient, i.e., about 5 dB; hence, the stabilityin the large-signal operation is less secured when compared with thecase in which the rat-race hybrid is adopted.

However, from another point of view, in the configuration of thepush-pull amplifier, the unitary amplifiers are mutually excited withthe reverse phases in the regular operation mode. Therefore, it can alsobe considered that the push-pull amplifier is easily odd-mode excited.Particularly, in the V-band, it is difficult even in the Wilkinson powerdistributing and coupling unit to form an isolation resistor showingsufficient isolation of at least 20 dB; therefore, for powerdistribution and coupling of the amplifier, it can be considered thatthe method intentionally adopting the push-pull-type parallel amplifierin which odd-mode excitation easily occurs is also effective.

The respective exemplary embodiments described above are favorableexemplary embodiments and can be modified in various ways within a scopeof the present invention.

This application is based upon and claims the benefit of priority fromJapanese patent application No. 2006-314700, filed on Nov. 21, 2006, thedisclosure of which is incorporated herein in its entirety by reference.

INDUSTRIAL APPLICABILITY

As described in conjunction with detailed and abundant examples, thecircuits or methods of the present invention are capable of correctlyobtaining the reflection coefficient (characteristic impedance) in thelarge-signal state of a circuit; hence, the circuits or methods make thedesign of the oscillator more precise as well as give us importantknowledge regarding the stability of a multistage amplifier, looposcillation in an amplifier, the stability of a balance-type amplifier,and the like. Therefore, the circuits or methods of the presentinvention advantageously contribute to the designs and evaluations of anamplifier, an oscillator, and the like which operates in a microwave ormillimeter-wave band.

BRIEF DESCRIPTION OF DRAWINGS

FIG. 1 is a diagram showing a circuit configuration of a relevantS-probe.

FIG. 2 is a diagram showing a general circuit configuration of aproposed no-loss S-probe.

FIG. 3 is a diagram showing a typical circuit configuration of aproposed no-loss S-probe.

FIG. 4 is a diagram showing a basic circuit configuration of anoscillator.

FIG. 5 is a diagram showing designs of oscillation start of anoscillator; (a) viewed at the gate terminal and (b) viewed at the drainterminal.

FIG. 6 is a diagram showing the analysis and the design of the negativeresistor.

FIG. 7 is a diagram showing the characteristic at stationary oscillationby the large-signal analysis.

FIG. 8 is a diagram showing the amplifier stability analysis by anS-probe.

FIG. 9 is a diagram showing detection (equivalent circuit) of even-modeoscillation in an S-probe method.

FIG. 10 is a diagram showing the small-signal characteristic of a 60 GHzamplifier.

FIG. 11 is a diagram showing the stability factor K of the 60 GHzamplifier.

FIG. 12 is a diagram showing the stability of the 60 GHz amplifier inthe even mode.

FIG. 13 is a diagram showing detection (equivalent circuit) of odd-modeoscillation by an S-probe method.

FIG. 14 is a diagram showing the stability (“without” balanced resistor)for odd-mode excitation of the 60 GHz amplifier.

FIG. 15 is a diagram showing odd-mode excitation (without balancedresistor) of the 60 GHz amplifier.

FIG. 16 is a diagram showing the stability (“with” balanced resistor)for odd-mode excitation of the 60 GHz amplifier.

FIG. 17 is a diagram showing an optimal design of the balanced resistorvalue.

FIG. 18 is a diagram showing comparison between the small-signal inputand the large-signal operation input.

FIG. 19 is a diagram showing the stability when a large signal isinputted.

FIG. 20 is a diagram showing a stability checking circuit configurationin a parallel-type amplifier.

FIG. 21 is a diagram showing the small-signal characteristic of aunitary amplifier.

FIG. 22 is a diagram showing the stability factor K of the unitaryamplifier.

FIG. 23 is a diagram showing a parallel amplifier employing a Y-branch.

FIG. 24 is a diagram showing the small-signal characteristic of theY-branch parallel amplifier.

FIG. 25 is a diagram showing the stability factor K of the Y-branchparallel amplifier.

FIG. 26 is a diagram showing the odd-mode stability of the Y-branchparallel amplifier.

FIG. 27 is a diagram showing a parallel amplifier using a Wilkinsonpower distributing and coupling unit.

FIG. 28 is a diagram showing the small-signal characteristic of theWilkinson-type parallel amplifier.

FIG. 29 is a diagram showing the stability factor K of theWilkinson-type parallel amplifier.

FIG. 30 is a diagram showing the odd-mode stability of theWilkinson-type parallel amplifier.

FIG. 31 is a diagram showing a balance-type amplifier using a 90-degreehybrid.

FIG. 32 is a diagram showing the small-signal characteristic of thebalance-type amplifier using a 90-degree hybrid.

FIG. 33 is a diagram showing the stability factor K of the balance-typeamplifier using a 90-degree hybrid.

FIG. 34 is a diagram showing the odd-mode stability of the balance-typeamplifier using a 90-degree hybrid.

FIG. 35 is a diagram showing a push-pull amplifier using a 180-degreehybrid.

FIG. 36 is a diagram showing the small-signal characteristic of thepush-pull amplifier using a 180-degree hybrid.

FIG. 37 is a diagram showing the stability factor K of the push-pullamplifier using a 180-degree hybrid.

FIG. 38 is a diagram showing the odd-mode stability of the push-pullamplifier using a 180-degree hybrid.

1. An RF circuit on a circuit simulator to be used in a microwave ormillimeter wave range or a high-frequency range, comprising a functionfor being inserted by a first port and a second port thereof in acircuit to be observed, at an arbitrary cross-sectional point of thecircuit, and evaluating a reflection coefficient (or a characteristicimpedance) in the cross section, wherein insertion loss between thefirst port and the second port is zero or approximately zero and isignorable also for any finite system impedance other than zero.
 2. TheRF circuit on a circuit simulator corresponding to claim 1, comprisingsix RF ports, wherein: a first resistor is connected from port 1 to anode a on the circuit, a second resistor is connected from the node a toa node b, a third resistor is connected from the node b to port 2, afourth resistor is connected from the node a to a node c, a fifthresistor is connected from the node b to a node d, and a sixth resistoris connected from the node b to a node e; a first DC block is connectedfrom the node c to port 6, a second DC block is connected from the noded to port 5, and a third DC block is connected from the node e to aground point (earth); a first voltage-dependent power source isconnected from port 3 to a ground point and a second voltage-dependentpower source is connected from port 4 to a ground point; assuming thatan instantaneous potential at the node a measured using as a referencethe node b of the second resistor is Vr, there is induced, at the sametime of occurrence of Vr, an instantaneous voltage of a magnitude of MVr(M is a real coefficient) in a direction from a ground point to the port3; and assuming that an instantaneous potential at the node b measuredusing as a reference the node e of the sixth resistor is Vb, there isinduced, at the same time of occurrence of Vb, an instantaneous voltageof a magnitude of Vb in a direction from a ground point to the port 4;and assuming that Rx is a positive real number, Rs is a positive realnumber and Rs>1, and a is a real coefficient; the second resistor has aresistance value of Rx, the first and third resistors have resistancevalues which widely include also negative resistance and which arerespectively −αRx and (α−1)Rx, a sum of them forms negative resistance−Rx and cancels out the second resistor Rx, which means that anarithmetic sum of the sum and the second resistor Rx is zero (theinsertion loss can be ignored); and further each of the fourth, fifth,and sixth resistance values is a resistance value Rs more than systemresistance.
 3. The circuit in accordance with claim 2, wherein the firstto sixth resistors are used at an environmental temperature set toabsolute zero degree (zero degree Kelvin).
 4. An evaluation method,characterized in that by inserting an RF circuit in accordance withclaim 1 by the first port and the second port in a circuit to beobserved, at an arbitrary cross-sectional point of the circuit andevaluating a forward or backward reflection coefficient (or acharacteristic impedance); and by assuming that the forward-viewreflection coefficient is Γ_(S) and the backward-view reflectioncoefficient is Γ_(L), an absolute value of a product therebetweenabs(Γ_(S)Γ_(L)) is or the absolute value of the product and a phaseangle of the product phase(Γ_(S)Γ_(L)) are employed as an index ofstability of the circuit to be observed.
 5. An algorithm on a circuitsimulator, characterized in that by inserting an RF circuit inaccordance with claim 1 by the first port and the second port in acircuit to be observed, at an arbitrary cross-sectional point of thecircuit and evaluating a forward or backward reflection coefficient (ora characteristic impedance); and by assuming that the forward-viewreflection coefficient is Γ_(S) and the backward-view reflectioncoefficient is Γ_(L), an absolute value of a product therebetweenabs(Γ_(S)Γ_(L)) or the absolute value of the product and a phase angleof the product phase(Γ_(S)Γ_(L)) is or are employed as an index ofstability of the circuit to be observed.
 6. A measuring method and adesigning method for electric circuits such as an amplifier and anoscillator employing an RF circuit in accordance with claim 1 and ameasuring method and a designing method for electric circuits such as anamplifier and an oscillator employing a method comprising by insertingthe RF circuit by the first port and the second port in a circuit to beobserved, at an arbitrary cross-sectional point of the circuit andevaluating a forward or backward reflection coefficient (or acharacteristic impedance); and by assuming that the forward-viewreflection coefficient is Γ_(S) and the backward-view reflectioncoefficient is Γ_(L), an absolute value of a product therebetweenabs(Γ_(S)Γ_(L)) is or the absolute value of the product and a phaseangle of the product phase(Γ_(S)ΓL) are employed as an index ofstability of the circuit to be observed.
 7. A measuring apparatus and adesigning apparatus for electric circuits such as an amplifier and anoscillator employing an RF circuit in accordance with claim 1 and ameasuring apparatus and a designing apparatus for electric circuits suchas an amplifier and an oscillator employing a method comprising byinserting the RF circuit by the first port and the second port in acircuit to be observed, at an arbitrary cross-sectional point of thecircuit and evaluating a forward or backward reflection coefficient (ora characteristic impedance); and by assuming that the forward-viewreflection coefficient is Γ_(S) and the backward-view reflectioncoefficient is Γ_(L), an absolute value of a product therebetweenabs(Γ_(S)Γ_(L)) is or the absolute value of the product and a phaseangle of the product phase(Γ_(S)ΓL) are employed as an index ofstability of the circuit to be observed.
 8. A recording medium havingrecorded therein a measuring method and a designing method in accordancewith claim
 6. 9. A measuring method and a designing method for electriccircuits such as an amplifier and an oscillator employing an RF circuitin accordance with claim 1 and a measuring method and a designing methodfor electric circuits such as an amplifier and an oscillator employing amethod comprising by inserting the RF circuit by the first port and thesecond port in a circuit to be observed, at an arbitrary cross-sectionalpoint of the circuit and evaluating a forward or backward reflectioncoefficient (or a characteristic impedance); and by assuming that theforward-view reflection coefficient is Γ_(S) and coefficient is Γ_(L),an absolute value of a product therebetween abs(Γ_(S)Γ_(L)) or theabsolute value of the product and a phase angle of the productphase(Γ_(S)Γ_(L)) is or are employed as an index of stability of thecircuit to be observed.
 10. A measuring apparatus and a designingapparatus for electric circuits such as an amplifier and an oscillatoremploying an RF circuit in accordance with claim 1 and a measuringapparatus and a designing apparatus for electric circuits such as anamplifier and an oscillator employing a method comprising by insertingthe RF circuit by the first port and the second port in a circuit to beobserved, at an arbitrary cross-sectional point of the circuit andevaluating a forward or backward reflection coefficient (or acharacteristic impedance); and by assuming that the forward-viewreflection coefficient is Γ_(S) and the backward-view reflectioncoefficient is Γ_(L), an absolute value of a product therebetweenabs(Γ_(S)Γ_(L)) or the absolute value of the product and a phase angleof the product phase(Γ_(S)Γ_(L)) is or are employed as an index ofstability of the circuit to be observed.
 11. An evaluation method,characterized in that by inserting an RF circuit in accordance withclaim 2 by the first port and the second port in a circuit to beobserved, at an arbitrary cross-sectional point of the circuit andevaluating a forward or backward reflection coefficient (or acharacteristic impedance); and by assuming that the forward-viewreflection coefficient is Γ_(S) and the backward-view reflectioncoefficient is Γ_(L), an absolute value of a product therebetweenabs(Γ_(S)Γ_(L)) is or the absolute value of the product and a phaseangle of the product phase(Γ_(S)ΓL) are employed as an index ofstability of the circuit to be observed.
 12. An evaluation method,characterized in that by inserting an RF circuit in accordance withclaim 3 by the first port and the second port in a circuit to beobserved, at an arbitrary cross-sectional point of the circuit andevaluating a forward or backward reflection coefficient (or acharacteristic impedance); and by assuming that the forward-viewreflection coefficient is Γ_(S) and the backward-view reflectioncoefficient is Γ_(L), an absolute value of a product therebetweenabs(Γ_(S)Γ_(L)) is or the absolute value of the product and a phaseangle of the product phase(Γ_(S)ΓL) are employed as an index ofstability of the circuit to be observed.
 13. An algorithm on a circuitsimulator, characterized in that by inserting an RF circuit inaccordance with claim 2 by the first port and the second port in acircuit to be observed, at an arbitrary cross-sectional point of thecircuit and evaluating a forward or backward reflection coefficient (ora characteristic impedance); and by assuming that the forward-viewreflection coefficient is Γ_(S) and the backward-view reflectioncoefficient is Γ_(L), an absolute value of a product therebetweenabs(Γ_(S)Γ_(L)) or the absolute value of the product and a phase angleof the product phase(Γ_(S)Γ_(L)) is or are employed as an index ofstability of the circuit to be observed.
 14. An algorithm on a circuitsimulator, characterized in that by inserting an RF circuit inaccordance with claim 3 by the first port and the second port in acircuit to be observed, at an arbitrary cross-sectional point of thecircuit and evaluating a forward or backward reflection coefficient (ora characteristic impedance); and by assuming that the forward-viewreflection coefficient is Γ_(S)and the backward-view reflectioncoefficient is Γ_(L), an absolute value of a product therebetweenabs(Γ_(S)Γ_(L)or the absolute value of the product and a phase angle ofthe product phase(Γ_(S)Γ_(L)) is or are employed as an index ofstability of the circuit to be observed.
 15. A measuring method and adesigning method for electric circuits such as an amplifier and anoscillator employing an RF circuit in accordance with claim 2 and ameasuring method and a designing method for electric circuits such as anamplifier and an oscillator employing a method comprising by insertingthe RF circuit by the first port and the second port in a circuit to beobserved, at an arbitrary cross-sectional point of the circuit andevaluating a forward or backward reflection coefficient (or acharacteristic impedance); and by assuming that the forward-viewreflection coefficient is Γ_(S) and the backward-view reflectioncoefficient is Γ_(L), an absolute value of a product therebetweenabs(Γ_(S)Γ_(L)) is or the absolute value of the product and a phaseangle of the product phase(Γ_(S)ΓL) are employed as an index ofstability of the circuit to be observed.
 16. A measuring method and adesigning method for electric circuits such as an amplifier and anoscillator employing an RF circuit in accordance with claim 3 and ameasuring method and a designing method for electric circuits such as anamplifier and an oscillator employing a method comprising by insertingthe RF circuit by the first port and the second port in a circuit to beobserved, at an arbitrary cross-sectional point of the circuit andevaluating a forward or backward reflection coefficient (or acharacteristic impedance); and by assuming that the forward-viewreflection coefficient is Γ_(S) and the backward-view reflectioncoefficient is Γ_(L), an absolute value of a product therebetweenabs(Γ_(S)Γ_(L)) is or the absolute value of the product and a phaseangle of the product phase(Γ_(S)ΓL) are employed as an index ofstability of the circuit to be observed.
 17. A measuring apparatus and adesigning apparatus for electric circuits such as an amplifier and anoscillator employing an RF circuit in accordance with claim 2 and ameasuring apparatus and a designing apparatus for electric circuits suchas an amplifier and an oscillator employing a method comprising byinserting the RF circuit by the first port and the second port in acircuit to be observed, at an arbitrary cross-sectional point of thecircuit and evaluating a forward or backward reflection coefficient (ora characteristic impedance); and by assuming that the forward-viewreflection coefficient is Γ_(S) and the backward-view reflectioncoefficient is Γ_(L), an absolute value of a product therebetweenabs(Γ_(S)Γ_(L)) is or the absolute value of the product and a phaseangle of the product phase(Γ_(S)ΓL) are employed as an index ofstability of the circuit to be observed.
 18. A measuring apparatus and adesigning apparatus for electric circuits such as an amplifier and anoscillator employing an RF circuit in accordance with claim 3 and ameasuring apparatus and a designing apparatus for electric circuits suchas an amplifier and an oscillator employing a method comprising byinserting the RF circuit by the first port and the second port in acircuit to be observed, at an arbitrary cross-sectional point of thecircuit and evaluating a forward or backward reflection coefficient (ora characteristic impedance); and by assuming that the forward-viewreflection coefficient is Γ_(S) and the backward-view reflection anabsolute value of a product therebetween abs(Γ_(S)Γ_(L)) is or theabsolute value of the product and a phase angle of the productphase(Γ_(S)ΓL) are employed as an index of stability of the circuit tobe observed.